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Transient behavior of regulated Brownian motion. I: Starting at the origin. (English) Zbl 0628.60083

This paper is the first of a series of two, studying the transient behaviour of regulated (that is to say, reflected) Brownian motion R as a model for the transient behaviour of stochastic flow systems. The objective is to obtain simple approximations for the moments of R. This paper considers the special case when R begins at zero.
After a lengthy discussion of results, an exposition is given of the construction of R using Skorokhod’s “reflecting barrier function”. Various probabilistic and Laplace-transform arguments are then applied, culminating in proposals for approximation of normalized moment functions by mixtures of exponentials. It is notable that the relaxation-time exponential approximation does not provide a useful fit for moderate time values.
Reviewer: W.S.Kendall

MSC:

60J65 Brownian motion
60J60 Diffusion processes

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